Answer: 6 %
Step-by-step explanation: 6 % of 12.5 = 0.75. 12.5 plus 0.75 = 13.25
MA.7.AR.4.1
Johnny and Eleanor went to their local gas station to collect information about the cost of
fuel for compact cars. They observed both regular and premium gas purchases that day and
recorded their data in the table below.
Gallons Purchased 11.5 7.2
10
14.3 6.8
9.7
Cost
$25.23 $15.80 $21.94 $40.63 $14.92 $27.56
Part A. Is there a proportional relationship between the number of gallons of gas sold and
the cost? Explain your answer.
Part B. If the relationship is not proportional, which data value or values should be
changed to make the relationship proportional? What could explain this
difference?
a) The fourth and sixth data points have significantly different ratios.
a) Let's calculate the ratios:
For the first data point:
= 11.5 gallons / $25.23 = 0.4555 gallons per dollar
For the second data point:
= 7.2 gallons / $15.80 = 0.4557 gallons per dollar
For the third data point:
= 10 gallons / $21.94 = 0.4556 gallons per dollar
For the fourth data point:
= 14.3 gallons / $40.63 = 0.3519 gallons per dollar
For the fifth data point:
= 6.8 gallons / $14.92 = 0.4555 gallons per dollar
For the sixth data point:
= 9.7 gallons / $27.56 = 0.3517 gallons per dollar
However, the fourth and sixth data points have significantly different ratios.
b) If the relationship is not proportional, the data values that should be changed to make the relationship proportional are the fourth and sixth data points.
The difference in ratios could be explained by factors such as fluctuations in gas prices or differences in gas grades.
To establish a proportional relationship, it would be necessary to collect data where the price per gallon remains constant for all data points or to separate the data based on gas grades and analyze each grade separately.
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estimate the original volume of the pyramid in fig 15.28 given that it's frustum has a 4 m by 4 m squared top which is 12 m vertically above the square base which is 20 m by 20 m (assume that the original problem was raised to a point . Neglect the volume of the entrance of the right of the photograph)
Answer:
Step-by-step explanation:
To estimate the original volume of the pyramid, we can use the formula for the volume of a frustum of a pyramid:
V = (1/3)h(a^2 + ab + b^2)
Where V is the volume, h is the height of the frustum, a is the side length of the top square, and b is the side length of the bottom square.
In this case, the top square has a side length of 4 m, and the bottom square has a side length of 20 m. The height of the frustum is 12 m.
Plugging these values into the formula, we get:
V = (1/3) * 12 * (4^2 + 4*20 + 20^2)
Simplifying the equation:
V = (1/3) * 12 * (16 + 80 + 400)
V = (1/3) * 12 * 496
V = 12 * 496/3
V = 1984
Therefore, the estimated original volume of the pyramid is 1984 cubic meters.
PLEASE HELP!!!!!!
it’s a division equation
Answer:
x+1
Step-by-step explanation:
you have to rewrite the equestion, factor the expression, and than reduce it
Find the y-intercept of the line 12x - 18y = -24.
Answer:
Therefore, the y-intercept of the line is (0, 4/3).
Step-by-step explanation:
To find the y-intercept of the line 12x - 18y = -24, we need to set x = 0 and solve for y.
12(0) - 18y = -24
Simplifying, we get:
-18y = -24
Dividing both sides by -18:
y = 4/3
Therefore, the y-intercept of the line is (0, 4/3).
Which expression is equivalent to 8.8x10^9/2.2x10^-3?
A 4 x 10^12
B 4 x 10^6
C 4 x 10^-3
D 4 x 10^-6
Consider a tree T with n vertices, where n is an odd integer greater than or equal to 3. Let v be a vertex of T. Prove that there exists a vertex u in T such that the distance between u and v is at most (n-1)/2.
Our initial assumption that for every vertex u in T, the distance between u and v is greater than (n-1)/2 must be false. Thus, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.
To prove that there exists a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can use a proof by contradiction.
Assume that for every vertex u in T, the distance between u and v is greater than (n-1)/2.
Since T is a tree with n vertices, it has n-1 edges. We can select a longest path P in T, which has a length of at least n-1. Let's denote the endpoints of this path as u and w, where u is the starting vertex and w is the ending vertex.
Now, consider the distance between u and v. Since we assumed that the distance between any vertex u and v is greater than (n-1)/2, the distance between u and v must be greater than (n-1)/2.
However, let's consider the distance between w and v. Since the path P is the longest path in the tree, the distance between w and v must be greater than or equal to the length of path P, which is at least n-1.
Now, let's consider the total number of vertices in the tree, which is n. Since n is an odd integer, (n-1)/2 is an integer as well.
If the distance between w and v is greater than or equal to n-1, and (n-1)/2 is an integer, then there must be a contradiction. This is because the distance between w and v is greater than (n-1)/2, violating our assumption.
Therefore, our initial assumption that for every vertex u in T, the distance between u and v is greater than (n-1)/2 must be false. Thus, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.
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What can be interpreted from the scatter plot above
The thing that can be interpreted from the scatter plot above is A. There is a negative association between number of hours of daily TV viewing and math quiz scores.
How to explain the scatterplotAs per given scatter plot, If the number of hour of daily TV viewing increases then the math quiz scores are decreases.
Hence, the number of hour of daily TV viewing and math quiz scores varies inversely.
Therefore, There is a negative ath association between number of hour of daily TV viewing and math quiz scores
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7. Given right triangle ABC below, determine sin(A).
The value of Sin A is 5/13.
Option A is the correct answer.
We have,
Sin A = Perpendicular / Hypotenuse
Sin A = BC / AB
And,
BC = 5
AB = 13
Substituting.
Sin A = 5/13
Thus,
The value of Sin A is 5/13.
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Help !!
centimeters and millimeters <3
1 cm = 10 mm. Length of book : 28 cm. Length of book = 280 mm. This shows that measurements in mm are the same but look to have a higher number .
How to compare centimeters and millimeters ?The conversion factor provided states that 1 cm is equal to 10 mm, which means that 1 cm is made up of 10 individual millimeters.
The length of my book in when measured in millimeters is 280 mm.
In centimeters, this is therefore:
= 280 mm / 10 cm /mm
= 28 cm
Although the numerical value appears higher when expressed in millimeters, it is important to note that the actual length of the book remains the same.
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#1 Write a positive or negative integer that represents the situation.
You run up 24 steps.
© 24
0-24
The integer number that represents the situation running up 24 steps is given as follows:
+24.
What are integer numbers?Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.
For altitudes, the signs are given as follows:
Gain of altitude: positive integer.Loss of altitude: negative integer.In this problem, we have an increase of altitude of 24 steps, hence the integer number is given as follows:
+24.
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Find the values of c guaranteed by the Mean Value Theorem (MVT) for f(x)=……..
Using the mean value theorem in f(x) = 1/2x² + 7, c = 2√3
What is the mean value theorem?The mean value theorem states that let f be continuous over the closed interval [a,b] and differentiable over the open interval (a,b). Then, there exists at least one point c ∈(a,b) such that f'(c) = [f(b) - f(a)]/(b - a)
To find c using the mean value theoren for f(x) = 1/2x² + 7 over the interval [0, 6], we proceed as follows.
Uisng the mean value theorem, we know that
f'(c) = [f(b) - f(a)]/(b - a)
⇒ f(c) = 1/(b - a)∫ₐᵇ[f(x)
Now over the interval [a, b] = [0,6]
f(c) = 1/(6 - 0)∫₀⁶[f(x)
Now, since f(x) = 1/2x² + 7
Substituting this into the equation, we have that
f(c) = 1/(6 - 0)∫₀⁶[f(x)
f(c) = 1/(6 - 0)∫₀⁶(1/2x² + 7)
f(c) = 1/6∫₀⁶(1/2x² + ∫₀⁶7)
f(c) = 1/6[1/2x³/3 + 7x]₀⁶
f(c) = 1/6[x³/6 + 7x]₀⁶
f(c) = 1/6[6³/6 + 7(6)] - [0³/6 + 7(0)]
f(c) = 1/6[6²+ 42] - [0 + 7(0)]
f(c) = 1/6([36 + 42] - [0 + 0])
f(c) = 1/6(78 - 0)
f(c) = 1/6(78)
f(c) = 13
Now, since f(x) = 1/2x² + 7
f(c) = 1/2c² + 7
1/2c² + 7 = 13
1/2c² = 13 - 7
1/2c² = 6
c² = 2 × 6
c² = 12
c = √12
c = 2√3
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A cyclist covers 5/7 of his route and an additional 40 minutes. He has yet to cover 118 miles less than 0.75 of his route. How long is his route?
The distance that describes how long his route was is: 168 miles.
How to determine the length of the routeTo determine how long the route was, we need to first represent the entire unknown distance covered by this individual with s.
5/7 s + 40 minutes + (0.75s - 118) = s
5/7s + 75/100s + 40 - 118 = s
5/7s + 75/100s - 78 = s
5/7s + 75/100s - s = 78
325s = 54600
s = 168 miles.
So, the entire distance covered by the cyclist is 168 miles.
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The distance that describes how long his route was is: 168 miles.
How to determine the length of the route.
To determine how long the route was, we need to first represent the entire unknown distance covered by this individual with s.
5/7 s + 40 minutes + (0.75s - 118) = s
5/7s + 75/100s + 40 - 118 = s
5/7s + 75/100s - 78 = s
5/7s + 75/100s - s = 78
325s = 54600
s = 168 miles.
So, the entire distance covered by the cyclist is 168 miles.
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Li Wei and Colleen have the same reading assignment. After one week Li Wei has read 90 pages and Colleen has read 126 pages. If Li Wei can you read 30 pages in an hour and Colleen henry 24 pages an hour, when will they be on the same page 
Equating the expressions, if Li Wei can read 30 pages in an hour and Colleen Henry 24 pages an hour, they will be on the same page in 6 hours.
What are equivalent expressions?Equivalent expressions are two or more algebraic expressions that have the same value when the variables are substituted with real numbers.
In this situation, we can determine the time that Li Wei and Colleen Henry can be on the same page by equating the expressions representing their reading rates.
The number of pages Li Wei can read in a week = 90
The number of pages Collen can read in a week = 126
Li Wei's reading rate per hour = 30 pages
Collen's reading rate per hour = 24 pages
Let the hours that Li Wei and Colleen can be on the same page= x
Expressions:The total number of pages Li Wei can read = 90 + 30x
The total number of pages Colleen can read = 126 + 24x
For Li Wei and Colleen to be on the same, the two expressions are equated.
90 + 30x = 126 + 24x
6x = 36
x = 6
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A young artist went to an art shop to buy a canvas. There were many sizes from which to choose. Some were standard sizes and some were custom-made. She wanted her next piece to incorporate the Golden Ratio, so she decided to buy the canvas whose dimensions most closely matched the Golden Rectangle. Here are the sizes that were available:
24" x 36"
24" x 40"
10" x 16"
26" x 16"
20" x 12"
Which canvas should the artist buy? Show your work.
The artist should buy the canvas with dimensions 26" x 16" as it most closely matches the Golden Rectangle.
To determine which canvas size most closely matches the Golden Rectangle, we need to calculate the aspect ratios of the available options and compare them to the Golden Ratio.
The Golden Ratio is approximately 1.618. A rectangle is considered to be a Golden Rectangle if its aspect ratio (width divided by height) is equal to the Golden Ratio.
Let's calculate the aspect ratios for each canvas size:
Canvas 1: 24" x 36"
Aspect ratio = 24 / 36 = 0.67
Canvas 2: 24" x 40"
Aspect ratio = 24 / 40 = 0.6
Canvas 3: 10" x 16"
Aspect ratio = 10 / 16 = 0.625
Canvas 4: 26" x 16"
Aspect ratio = 26 / 16 = 1.625
Canvas 5: 20" x 12"
Aspect ratio = 20 / 12 = 1.667
Now, let's compare the aspect ratios of the available options with the Golden Ratio (1.618) to see which one is closest:
Canvas 1: |0.67 - 1.618| = 0.948
Canvas 2: |0.6 - 1.618| = 1.018
Canvas 3: |0.625 - 1.618| = 0.993
Canvas 4: |1.625 - 1.618| = 0.007
Canvas 5: |1.667 - 1.618| = 0.049
The canvas with the aspect ratio closest to the Golden Ratio is Canvas 4: 26" x 16". Its aspect ratio of 1.625 is only 0.007 away from the Golden Ratio.
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Students were asked their favorite ice cream flavor. The results showed that 196 students selected vanilla as their favorite ice cream flavor. This represents 49% of the total number of students surveyed. What was the total number of students surveyed?
I need the answer and explanation!!!
Answer:
The total number of students surveyed is 400.
Step-by-step explanation:
We want to know that 49% of what number is 196
Let x = the total number of students
.49x = 196 (49% as a decimal is .49) Divide both sides by .49
x = 400
Evaluate the following statement.
( - 179 – 78 ) + 41 - ( - 165 )
The answer is:
( - 179 – 78 ) + 41 - ( - 165 )
=-51
Answer:
(-257) +41+165
-257+206
-51
Urgent!!!
cos4α + 2 Sin² 2α
Answer:
Step-by-step explanation:
cos4α + 2 Sin² 2α is a trigonometric expression that involves the cosine and sine functions of the angle α. This expression can be simplified using trigonometric identities to get:
cos4α + 2 Sin² 2α = (cos² 2α)² + 2 (Sin 2α)²
This simplification involves using the double angle identity for sine and the identity for the square of cosine.
Brainliest Pls
Answer:1
Step-by-step explanation:
cos(4α) + 2sin²(2α)
First, let's expand cos(4α)
cos(4α) = cos²(2α) - sin²(2α)
Now, let's substitute this expression back into the original equation:
cos(4α) + 2sin²(2α) = (cos²(2α) - sin²(2α)) + 2sin²(2α)
= cos²(2α) + sin²(2α)=1 by
cos²(α) + sin²(α)=1
Un fabricante de bombillas gana 0,60€ por cada bombilla que sale de fábrica pero pierde 0,80€ por cada una que sale defectuosa. Un determinado día en el que fabrico 2.100 bombillas obtuvo un beneficio de 966€. ¿Cuántas bombillas de cada tipo fabricó?
The manufacturer made 1,890 non-defective light bulbs and 210 defective light bulbs.
How many defective and non-defective light bulbs was made?Let represent number of non-defective light bulbs with x
Let represent number of defective light bulbs with y.
The profit from selling non-defective light bulbs is €0.60x
The loss from selling defective light bulbs is €0.80y.
Given that the manufacturer made a profit of €966, we can form the equation:
0.60x - 0.80y = 966 ---(1)
The total number of light bulbs produced is 2,100, so we have:
x + y = 2,100 ---(2)
To solve this, we will use method of elimination.
We multiply equation (2) by 0.60.
0.60x + 0.60y = 1,260 ---(3)
Now, subtract equation (3) from equation (1):
0.60x - 0.60x - 0.80y - 0.60y = 966 - 1,260
-1.40y = -294
y = -294 / -1.40
y = 210
Substituting value of y into equation (2):
x + 210 = 2,100
x = 2,100 - 210
x = 1,890.
Translated question:
A light bulb manufacturer earns €0.60 for each bulb that leaves the factory but loses €0.80 for each one that is defective. On a certain day when he manufactured 2,100 light bulbs, he made a profit of €966. How many light bulbs of each type did he make?
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What is the meaning of "possibly some ui are not free, or even do not occur, in ϕ"?
The phrase "possibly some ui are not free, or even do not occur, in ϕ" refers to a logical formula or expression ϕ that contains variables ui.
Answer to the aforementioned questionWhen it says "possibly some ui are not free," it means that not all of the variables ui in ϕ are unrestricted or unconstrained. Some of them may have certain conditions or restrictions placed on them within the context of the formula ϕ.
On the other hand, when it says "or even do not occur, in ϕ," it means that some variables ui may not appear at all in the formula ϕ. This implies that those variables are not present or relevant in the expression ϕ and do not play a role in its interpretation or evaluation.
In summary, the phrase indicates that in the formula ϕ, some variables ui may have restrictions or conditions placed on them, while others may not be present or relevant within the context of the formula.
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2/3x - 1/5x = x - 1
solve pls
.....................................................................
Answer:
b
Step-by-step explanation:
Answer:
The correct statement is: The temperature of the object is decreasing exponentially by 0.007% each minute.
Step-by-step explanation:
The exponential term in the function, [tex]e^{0.007 h}[/tex], is greater than 1. This means that the temperature is increasing over time.
However, the exponent is very small, so the increase in temperature is very slow. In fact, the temperature is increasing by only -0.007% each minute.
We can use the following formula to calculate the percent change in temperature each minute.
[tex]\boxed{\bold{Percent\: change = \frac{(new \:value - \:old \: value) }{ old\:value }* 100\%}}[/tex]
In this case, the new value is the temperature after one minute, and the old value is the temperature at the start of the minute.
So, the percent change in temperature is:
[tex]= \frac{10 + 160e^{-0.007 * 1} - 10) }{ 10} * 100\%[/tex]
≈ -0.007%
Therefore, the temperature of the object is decreasing exponentially by 0.007% each minute.
50 Points! Multiple choice algebra question. Photo attached. Thank you!
The angle that is not a solution to the trigonometric equation sin(2θ) = 1 is given as follows:
a) 90º.
How to solve the trigonometric equation?The trigonometric equation in the context of this problem is defined as follows:
sin(2θ) = 1
The sine assumes a value of 1 at:
90º.
Hence the solution is obtained as follows:
2θ = 90º.
θ = 45º.
The equivalent angle to 45º on the third quadrant is given as follows:
180º + 45º = 225º.225 - 360 = -135º.Hence 225º and -135º are also solutions to the trigonometric equation.
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Plssssss helllllp meeee 50.point and will mark Brainlyiest Solve: 4!
A.16
B.6
C.24
D.4
Answer:
C
Step-by-step explanation:
the expression ! ( factorial ) has the following meaning
n! = n(n - 1)(n - 2) ... × 3 × 2 × 1
Then
4! = 4 × 3 × 2 × 1 = 24
pls help it is due today
The property that should be used to simplify the expression 1/t⁻³ is [tex]\frac{1}{a^-m}[/tex] = [tex]a^m[/tex] (where a ≠ 0). Option A
How to identify the property to simplify the expression?In the given scenario or expression, this property implies that 1/t⁻³ = t³. The negative exponent in the denominator becomes a positive exponent when moved to the numerator.
Here is the step-by-step solution
1/t⁻³ = 1/(t⁻³)
1/(t⁻³) = (t⁻³)⁻¹
(t⁻³)⁻¹ = t⁽⁻³⁾ˣ⁽⁻¹⁾
t⁽⁻³⁾ˣ⁽⁻¹⁾ = t³
Therefore, the simplified expression is t³.
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2/5 of Jim's savings is equal to 4/9 of Max's savings. Jim has $30 more than Max. 5 How much money does Max have?
As Jim has $30 more than Max, as per this, Max has $270.
Let's assume Max's savings as 'x' dollars.
We have:
2/5 of Jim's savings is equal to 4/9 of Max's savings.
(2/5) * Jim's savings = (4/9) * Max's savings
We also know that Jim has $30 more than Max.
Jim's savings = Max's savings + $30
So,
(2/5) * Jim's savings = (4/9) * Max's savings
(2/5) * (Max's savings + $30) = (4/9) * Max's savings
To solve for Max's savings, we can solve this equation:
(2/5) * (x + $30) = (4/9) * x
So, for x:
(2/5) * (x + $30) = (4/9) * x
Multiplying both sides by 45 (the least common denominator of 5 and 9) to eliminate the fractions:
18(x + $30) = 20x
18x + 540 = 20x
540 = 20x - 18x
540 = 2x
x = 270
Therefore, Max has $270.
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A Park is shaped like a trapezoid. It has an area of 7.2 mi.² one piece is 1.2 miles on the other bases 2.4 miles long. What is the height of the trapezoid
(Can't delete my answer)
A sales person starts working 40 hours per week at a job with 2 options for being paid . Option A is an hourly wage of $19. Option B is a commission rate of 8% on weekly sales.
How much does the sales person need to sell in a given week to earn the same amount with each option?
A. $9,500
B. $4,750
C. $760
D. $320
Given, Option A: Hourly wage is $19 and the salesperson works 40 hours per week. So, he will earn in a week [tex]\sf = 19 \times 40 = \$760[/tex]
Now, according to option b, he will get 8% commission on weekly sales.
Let. x = the amount of weekly sales.
To earn the same amount of option A, he will have to equal the 8% of x to $760
So, [tex]\sf \dfrac{8x}{100}=760[/tex]
Or, [tex]\sf 8x= 76000[/tex]
Or, [tex]\sf x= \dfrac{76000}{8}=9500[/tex]
the salesman needs to make a weekly sales of $9,500 to earn the same amount with two options.
The mean of three test is 74 what must be the the 4th score to get a mean of 78?
To achieve a mean of 78 with four scores, the fourth score must be 90.
We need to consider the current mean, the number of tests, and the desired mean in order to find the fourth score needed to achieve a mean of 78
Let's assume the three test scores are x1, x2, and x3.
We know that the mean of these three scores is 74. So we can assume that
The sum of these numbers is 74 or
(x1 + x2 + x3)/3 = 74
Let's denote it as x4 ,to find the fourth score we will use the formula to calculate the mean:
(x1 + x2 + x3 + x4)/4 = 78
To solve for x4, we can rewrite it as:
x1 + x2 + x3 + x4 = 78 * 4
Now, we can substitute the value of the mean of the first three scores into the equation:
(x1 + x2 + x3) + x4 = 312
we know that,
(x1 + x2 + x3) = 3 * 74
or,
3 * 74 + x4 = 312
Simplifying this, we get:
222 + x4 = 312
Subtracting 222 from both sides:
x4 = 312 - 222
x4 = 90
Therefore, to achieve a mean of 78 with four scores, the fourth score must be 90.
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Please help it’s due today!!!!
4. RSTU is a trapezoid because the opposite sides RS and UT are parallel.
5. RSTU is not an isosceles trapezoid because the diagonals are not congruent.
How to verify that RSTU is a trapezoid?In order to verify that RSTU is a trapezoid, we would have to determine slope of the pair of opposite sides and check whether at least one pair of opposite sides are parallel;
RU ║ ST
Slope of side RU = Slope of side ST
Slope of RU = (y₂ - y₁)/(x₂ - x₁)
Slope of RU = (1 + 3)/(5 + 3)
Slope of RU = 4/8
Slope of RU = 0.5.
Slope of RS = (y₂ - y₁)/(x₂ - x₁)
Slope of RS = (-9 + 3)/(-4 + 3)
Slope of RS = -6/-1
Slope of RS = 6.
Slope of ST = (y₂ - y₁)/(x₂ - x₁)
Slope of ST = (-2 - 1)/(10 - 5)
Slope of ST = -3/5
Slope of ST = -0.6.
Slope of UT = (y₂ - y₁)/(x₂ - x₁)
Slope of UT = (-2 + 9)/(10 + 4)
Slope of UT = 7/14
Slope of UT = 0.5.
Therefore, RSTU is a trapezoid because the opposite sides RS and UT are parallel.
Question 5.
In order to determine whether RSTU is an isosceles trapezoid, we would have to determine length of the diagonals by using the distance formula and check whether they are congruent;
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance RT = √[(-2 + 3)² + (10 + 3)²]
Distance RT = √170 units.
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance US = √[(5 + 4)² + (1 + 9)²]
Distance US = √181 units.
Therefore, RSTU is not an isosceles trapezoid because the diagonals RT and US are not congruent.
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Can someone please answer and provide an explanation for these problems?
Answer:
details:
54)Write the midpoint formula::
Substitute
into
::
Swap the sides:
Swap the sides:
Multiply both sides of the equation by the common denominator:
Reduce the fractions:
Multiply both sides of the equation by the common denominator:
Reduce the fractions:
Calculate the product or quotient:
Rearrange variables to the left side of the equation:
Calculate the sum or difference:
Express solutions in ordered pairs::
(55)Write the midpoint formula::
Substitute
into
::
Swap the sides:
Swap the sides:
Multiply both sides of the equation by the common denominator:
Reduce the fractions:
Multiply both sides of the equation by the common denominator:
Reduce the fractions:
Calculate the product or quotient:
Rearrange variables to the left side of the equation:
Calculate the sum or difference:
Express solutions in ordered pairs::
(56)Write the midpoint formula::
Substitute
into
::
Swap the sides:
Swap the sides:
Multiply both sides of the equation by the common denominator:
Reduce the fractions:
Multiply both sides of the equation by the common denominator:
Reduce the fractions:
Calculate the product or quotient:
Rearrange variables to the left side of the equation:
Calculate the sum or difference:
Express solutions in ordered pairs::
(57)Write the midpoint formula::
Substitute
into
::
Swap the sides:
Swap the sides:
Multiply both sides of the equation by the common denominator:
Reduce the fractions:
Multiply both sides of the equation by the common denominator:
Reduce the fractions:
Calculate the product or quotient:
Rearrange variables to the left side of the equation:
Calculate the sum or difference:
Express solutions in ordered pairs::